The topic of reliable signal transmission at very low Signal-to-Noise Ratio (SNR) has recently become of interest in the context of machine communication in a cellular communications network. For example, an appliance in a home basement would need an extra 20 decibels (dB) of link margin to communicate with an outdoor base station. Note that this very low SNR theme was also an active topic in the context of mobile and satellite communications some years ago, resulting in a solution called high penetration paging.
The basic question that must be addressed is what modulation scheme, i.e., coherent or non-coherent, works best at very low SNR. Somewhat surprisingly, the answer is unclear, as classical communication theory essentially addresses high SNR operation. In a coherent scheme, a transmitter transmits a non-differential modulation along with pilots, and a receiver uses pilot-aided demodulation, consisting of channel estimation over the pilots to obtain knowledge of Channel State Information (CSI), followed by coherent demodulation. The CSI includes a channel estimate for a wireless communication channel between the transmitter and the receiver. In contrast, in a non-coherent scheme, a transmitter uses a differential modulation, and a receiver uses a differential demodulator. A non-coherent scheme does not require pilot transmission or knowledge of CSI.
Assuming a coherent scheme, the issue then becomes achieving reliable communication at very low SNR. Here, SNR is from the perspective of the signal, while performance is from the perspective of the bits transmitted within the signal. That is, SNR is the ratio of signal power to noise power, and performance is the bit or block error rate. From this perspective, given a modulation choice, e.g., Quadrature Phase Shift Keying (QPSK) or 16 Quadrature Amplitude Modulation (16-QAM), and a certain fixed SNR, suppose that the performance is unreliable. Then, one way to boost the performance at the fixed SNR is to accumulate more energy per bit. This is achieved with coding such as repetition, which is the simplest form of coding. More complex coding schemes can also provide some coding gain on top of the energy gain of repetition. But at low SNR, a low rate coding is needed, which effectively becomes repetition.
Repetition schemes transmit the same modulation symbol multiple times. If the channel is highly correlated across repetitions, then channel estimation can be improved. However, in the extreme case where the channel is independent across repetitions, there is no improvement in channel estimation from the repetitions. Nevertheless, overall performance will improve. The general case where the channel is correlated follows naturally in a similar way. Note that repetition is technically the same regardless of whether the repetition is in time, in frequency, or by receiving on multiple antennas. Also, correlation in time, frequency, or across multiple receive antennas, or lack of it, can be captured in the same manner. Therefore, these scenarios are interchangeably referred to herein as a Single Input Multiple Output (SIMO) scheme.
One issue with the coherent scheme is that current coherent demodulation schemes (e.g., a Maximum Likelihood (ML) receiver) assume a channel estimate at the receiver that is noiseless. However, particularly at very low SNR, this assumption is incorrect. As such, there is a need for systems and methods for improved coherent demodulation in the presence of noisy CSI and, in particular, in the presence of noisy channel estimation.